It was Krein [1]}, [2]} who first introduced the matrix extensions of scalar orthogonal polynomials. On this topic, there have been some relevant papers published afterward [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, as well as more recent contributions, including for instance [11]}, [8]}.
Numerous findings have been made such as scattering problem resolution and matrix Favard theorem [13]}.
Later, it was proven that matrix orthogonal polynomials sometimes satisfy some properties as do the classical orthogonal polynomials, such as the scalar type Rodrigues' formula [14]}, [15]}.
Moreover, the last few years have seen the discovery of a plethora of families of orthogonal matrix polynomials that are eigenfunctions of certain fixed second order linear differential operators with a matrix coefficients independent of the orthogonal polynomial degree [16]}, [17]}, [18]}.
